Quantum Dynamics

Up to this point, we have discussed the basic principles of quantum mechanics, including the postulates and mathematical formalism. We have not yet discussed how quantum systems evolve in time. There are typically three ways to describe the time evolution of quantum systems. The first is the Schrödinger picture, where the state of the system, , evolves in time. The second is the Heisenberg picture, where the operators themselves evolve in time. The third is a different approach called the path integral formalism developed by Richard Feynman.

📄️ Time Evolution of Quantum Systems

In this section, we will derive the third postulate of quantum mechanics, which requires that the time evolution of quantum systems be governed by a unitary operator.

📄️ Elementary Examples of Schrödinger Picture

In this section, we will explore a few elementary examples of the Schrödinger picture that we introduced in the previous section.

📄️ The Heisenberg Picture

Previously, we have used the Schrödinger picture to describe the dynamics of a system.

📄️ Feynman Path Integrals

The Feynman path integral formulation of quantum mechanics is a powerful and elegant way to describe the dynamics of quantum systems.

📄️ Quantum Simple Harmonic Oscillator

The quantum simple harmonic oscillator is a fundamental model in quantum mechanics that describes the behavior of a particle in a potential well.